# Induced surface charge distribution

• Raihan amin
In summary, two identical metallic spherical conductors with radii ##R## are placed at a distance ##d## apart. One conductor has a charge of ##Q## while the other is neutral. To determine the induced charge on the neutral conductor, an image charge ##q## is placed inside it and the potential at the surface is calculated using the equation $$V = {\frac {Q} {r_1} }+\frac {q}{r_2}$$. However, the general solution for two conducting spheres is complex and an easier solution is only possible if one of the conductors is grounded, which is not the case here.
Raihan amin
OP warned about not using the homework template
Two identical metalic spherical conductor of radii ##R## are at a distance ##d## apart.One of the conductor has charge ##Q## while the another one is neutral.What will be the induced charge on the other conductor ?

If we put an image charge ##q## inside the neutral one. Then the potential at the surface is $$V = {\frac {Q} {r_1} }+\frac {q}{r_2}$$
So $$V=\frac {Q}{\sqrt {R^2 +d^2 -2Rdcos {\theta}}} + \frac {q}{\sqrt {R^2 + d'^2 - 2Rd' cos{\theta}}}$$
Now I know that the suface of the spherical conductor will be equipotential,independent of ##\theta##
Here i consider the other charge as a point particle.but I can't find V.Still i don't know whether the image charge method will do or not.

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The general solutionn for two conducting spheres is quite complicated. See e.g. https://arxiv.org/pdf/0906.1617.pdf.
I recall it is a lot simpler if one is grounded, but I gather that is not the case here. Don't know whether it helps that one has net zero charge.

Raihan amin

## 1. What is induced surface charge distribution?

Induced surface charge distribution is the redistribution of electric charges on the surface of a material due to the presence of an external electric field.

## 2. How does induced surface charge distribution occur?

Induced surface charge distribution occurs when an external electric field causes the electrons in a material to shift and accumulate on one side, creating a temporary charge separation.

## 3. What factors affect the magnitude of induced surface charge distribution?

The magnitude of induced surface charge distribution is affected by the strength of the external electric field, the properties of the material (such as its dielectric constant), and the geometry of the material.

## 4. What are some real-life applications of induced surface charge distribution?

Induced surface charge distribution has many practical applications, such as in capacitors, where it helps store and release electrical energy, and in electrostatic precipitators, where it is used to remove pollutants from industrial exhaust gases.

## 5. How is induced surface charge distribution related to surface potential?

Induced surface charge distribution and surface potential are closely related, as the presence of induced charges on a material's surface can affect its surface potential and vice versa. The distribution of surface charges can also be used to measure the surface potential of a material.

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